List questions from birational-geometry

Published on 25 Apr 2021 - 17:34

87

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Why the curve is rational?

Published on 02 May 2021 - 16:04

168

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Why $X$ is a del Pezzo surface?

Published on 09 May 2021 - 13:25

1.2k

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Nef and semiample divisor

Published on 12 May 2021 - 13:42

132

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Why the pencil of planes on quadric $Q\subset\mathbb{P}^4$ cuts out on cubic $V\subset\mathbb{P}^4$ a pencil of elliptic curves $|E|$?

Published on 25 Mar 2026 - 9:18

26

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Why the image of a minimal surface $S$ ($\kappa(S)=1$) defined by a linear system $|M|$ is a curve?

Published on 16 May 2021 - 22:05

78

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Finite Abelian subgroups of $Aut(\mathbb{P}_{\mathbb{C}}^2)$

Published on 18 May 2021 - 0:40

456

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Question with the definition of rational maps (Algebraic geometry)

Published on 20 May 2021 - 13:38

83

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Hyperplane $\Phi_X$ in Chow construction (Algebraic Geometry by Joe Harris)

Published on 06 Jun 2021 - 21:38

155

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Historical references for Birational Geometry.

Published on 16 Jun 2021 - 13:59

76

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Criterion for dominant rational map and linear independence of global sections

Published on 21 Jun 2021 - 0:15

153

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Direct image sheaf and sheaf of direct image (of divisors)

Published on 28 Jun 2021 - 17:18

325

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How close are birational surfaces to being isomorphic?

Published on 01 Jul 2021 - 10:34

211

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How to show divisoral sheaf is rank one?

Published on 06 Jul 2021 - 6:41

179

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On the Picard group of the generic fiber

Published on 15 Jul 2021 - 10:04

List Question

Every birational map is an isomorphism for algebraic curves

Why the curve is rational?

Why $X$ is a del Pezzo surface?

Nef and semiample divisor

Why the pencil of planes on quadric $Q\subset\mathbb{P}^4$ cuts out on cubic $V\subset\mathbb{P}^4$ a pencil of elliptic curves $|E|$?

Why the image of a minimal surface $S$ ($\kappa(S)=1$) defined by a linear system $|M|$ is a curve?

Finite Abelian subgroups of $Aut(\mathbb{P}_{\mathbb{C}}^2)$

Question with the definition of rational maps (Algebraic geometry)

Hyperplane $\Phi_X$ in Chow construction (Algebraic Geometry by Joe Harris)

Historical references for Birational Geometry.

Criterion for dominant rational map and linear independence of global sections

Direct image sheaf and sheaf of direct image (of divisors)

How close are birational surfaces to being isomorphic?

How to show divisoral sheaf is rank one?

On the Picard group of the generic fiber

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